Tuesday, December 21, 2010

*click to enlarge diagram. "back" to return. Wishing you all a very happy christmas and a bright New Year in 2011.

Love is the strongest Power in the universe.
Some of us feel so traumatised and distressed at times that it feels a most difficult thing to love anyone or anything. At least we can try; practise the Form, and the reality may follow. The Dalai Lama is our shining example. Especially the most troublesome people need love, for that is ultimately the only remedy for our human tragedies. Peace on Earth and Goodwill to all men and women and children and Sentient beings and even to non sentient beings. Alleluja.

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27/12/2014 Thank you to all the people who visit this here Page at Christmas Time over the years. This year there is a crocheted Cone like a Tree and more interesting information. Happy 2015 to ALL.

Monday, December 20, 2010

*please note: these tables begin with F(n) : F1 is 0, F2 is 1, F3 is 1, F2 is 2, etc. Most other websites begin with F0 is 0, F1 is 1, F2 is 2 etc. Therefore my calculations are one out.Please noteThere is an error in addition in F81. It should be 23 416 728 348 467 685and also in F99. It should be 135 301 852 344 706 746 049. All the nearby numbers need correction also.What is signifant about 192?

I have begun an ambitious model, F21 = 6765, already completed, for a seashell, next row will be 10946 stitches, if I can bear to finish it.I wondered how long is this edge, so I measured 1000 stitches and it was about 208cm.192 cm is very close to 208.

Sunday, November 21, 2010

It has been a long time since I posted any new items. In a caravan with no electricity and no mobile phone reception there is no way of having my own computer, not even with wifi.
In the meantime the Australian Museum in Sydney was kind enough to show a display of mine for 2 weeks as part of the Alive! Exhibition on biodiversity, in September.

Summer is coming and the wild oats are up to 8 ft tall. I am having trouble looking after 4 acres of land by myself working only with hand tools. Pink and red bush roses are abundantly in flower after the unusual rains of winter and spring. Chocolate lilies ( yes they do have this perfume) are flowering in grassy woodland remnants.

Mindful of last year's devastating bushfires I am publishing the equations I have found in connection with the Fibonacci Series. If my caravan were to burn down then all my papers and models would be lost. I am only briefly noting them. There is a lot to document and it might be a slow process. So here goes:-

7. F(n) = 5F(n-6) + 8F(n-5).... ditto
........................................................................................8. The following are spookily exact especially at the higher numbers, not always so at lowest iterations:-

****This is Phi, a "transcedental number", 1.6180339887498
The golden mean is 1:618
or 2:3:5

****There is a most extraordinary websitehttp://www.humanresonance.org/
The author Alexander Putney has written a book on Phi. One can read it online for free.

NB. 5/2013 Incredibly, this website has been stolen! The author had to buy a new web domain.
It is http://www.human-resonance.org...................................................................................

Sunday, August 15, 2010

This crochet model is the shape formed for 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. That is the shape of the web of ancestors for one single person, for 200 years, or 10 generations.
Extend that out further into 20,000 years and more.....
Multiply by the number of people on earth now.
There will be merging of ancestors for siblings.
Every time two people are married, there is merging of ancestral lineages.For that matter, there would be merging of ancestors each time two people have sex, especially if there is a child conceived.

From the previous population graph, there will be a limit to the number of ancestors possible. Somewhere further along is the Common ancestor, the UR mother and the UR father. My guess is that there may be more than one seed person ancestor, one for each human type group, eg asian, african, aboriginal, european, maybe siberian or from Altai Mountains area. DNA and deep ancestry investigations are interesting.

Are we One big family or a number of different families?

More 12/6/2014. It has taken me so long to publish this!

on its way....

Please click on image to enlarge it.

It seems as if the planet was seeded by a number of different races-----so I don't think we are related to everyone on the planet back in 1400s.........

The Tree of Life has many dead and broken branches.
Said by Charles Darwin.

So also has the Tree of Man. Plague, wars, famine and climate change has trimmed the tree over aeons. It is a miracle that we are still here. It is possible that we might discover a way to consciously make this a happy world that can live forever.

Monday, June 28, 2010

The important message is - it looks like world population is doing a flip!

Click photo to enlarge to full page size, and click back to return to text.

.........

Some say that the megacities will save us and that the population of the world will stabilise at 9 billion in 2050

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PS. 27/8/2010 My friend tells me that the population graph is not clear.

The straight line to northeast is the 2, 4, 8, 16, 32 etc; this is ancestor line

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It intersects the population line and that is the point of maximum number of ancestors possible for one person. The common ancestors must be part of merging sooner in time, then merging to form limbs and trunk of human family tree(s).

PS 27/8/2010 There was a quote from an article on collapsing societies, eg the Anasazi, ie "The rich reserve for themselves the right to die last". This is a cue to live symbiotically and sustainably on planet earth.

make a leaf by knitting 5, then 3, then2, then 1, then add it to stem, knitting both together, and doing some more chains to lengthen stem,

Finish off. Sew flower part together in colour. Sew green sepal part together.

Make more of these and have a bunch of pretty flowers.

I used number 12 knitting needles and 1 or 2 ply fine tapestry wool (English, Applemore) but you can use any yarn at all. You could crochet them also, I guess, working from 1 stitch and reading the pattern backwards, increasing, knit 2 together to get 5, 10, 15, 25. (5x 1, 2, 3, 5.)

I do hope this pattern is OK to understand. It is Fibonacci again, ie, 1, 2, 3, 5.

***2/1/2015 I have re posted this Pattern recently in "some people and the models they make"
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John Gribbin wrote a fine book, "Deep Simplicity" and he discussed the Bifurcating Series.

Two dimensional graphs show chaos after 3 generations. I won't go on about it just now because I am far from home, writing this up at a Youth Hostel in Sydney, and I don't have my notes.

Dr Taimina is magically able to create shapes that the usual Euclidean Geometry cannot describe. It is to crochet that we turn.

Here is what 1, 2, 4, ........512, looks like.

It shows a butterfly shape when configured.

But.... there are at least 12 other possible configurations, and I need to draw them for a later post.

Now we have a model up to 1024 stitches on the outer row:-
4 spirals; very elegant.

Not only that, folks, it goes on to 16000 and 320000 or so:-

When crocheting I need to use the longer stitch, a treble or double treble crochet as this is easier to configure into complex spirals. The single crochet or half treble make for much more compact models, nice when making seashells.

OK, This shows that one can go on forever, the only constraining factors are the size of the room or the Universe, and the quantity of raw material available.

Where is the conundrum?
It'll be obvious when I post the graph of this series against hyperbolic axes graph.What has happened regarding our ancestors back in time?

After 1000 years there have been 50 generations
and 10 to the power 15 ancestors, a quadrillion, clearly an impossibility.

1000 years ago there were only half a billion humans on Earth, or so.

In about 1400, 600 years ago, the two lines intersect,
graph in next posts,
so there can never be more than a billion ancestors.

I checked it out on the Internet, on Yahoo! Answers,
One person observed that the family lineages merge,
like branches and limbs and trunk of a tree.
This question has not been solved, not yet.

I would love to ask Anastasia or Volodhya.
They are mathematically absolutely fast in their speed of thinking.
See Book 6 of The Ringing Cedar Series, "The Book of Kin".
On pages 58, 59 Volodhiya observed that in a living system, 1+1=3.
mother + father make child .
There is clearly a new way of looking at maths.

An Idea: One day I (or anyone) might make a giant clam with deeply wavy lips, made in hemp string, knitted with 1 metre dowelling "knitting needles" and covered with Roman hydraulic cement (fine powdered clay and cement with minimal water added until it forms a gel= great material for sculpture.) A pinky grey satin pillow could be included for clam's inside body, and a big "pearl "could be embedded in the shell!

***** NB. As far as I am concerned, none of this work of mine is copyright.

The Fibonacci Series belongs to Great Nature and thus belongs to anyone who is interested to use it creatively and happily. Enjoy!

I am awaiting permission from the publishers to use 3 photos of seashells with identifications, from "Australian Seashores in Colour" by Keith Gillettt and John Yaldwyn, a 1969 publication, dedicated to their mentors and colleagues Elizabeth Carrinton Pope and the late Frank Alexander McNeil, from the Australian Museum.

It seems the publisher AH&W Reed may no longer exist, so it is a problem to know what to do.

There is more work to do with vortexes and ripples, using the maths of Fibonacci series to make the models. The shapes have been made, they just need to be documented as they soon will be.

I would like to digress for a while, away from the Fibonacci series, to the Bifurcating series,

1, 2, 4, 8, 16, 32, 64, 128 etc. and to the Series which are Powers of 5 and of 10 which make very interesting models.

Monday, June 21, 2010

Back in July 2007 I needed to find a sequence within the series which was amenable to crochet or knitting patterns. Above is a photo of a page from my Journal to illustrate. Another page from my Journal is above it. Click to enlarge to full size. Then go back to main text.

It was evident that 2 times F(n-2) plus F(n-3) was the Pattern.

eg 610=2x233+144

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The yellow and beige model was the very first one I made-

in the photo it is 377 stitches crocheted on the outer edge.

The model below is 144 stitches on the outer edge.

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The second photo is of the models folded in half.

The 144 model looks like a bracket fungus, or like a pouch!

One thinks of endoderm, ectoderm etc and invagination--

the beginnings of cell division, maybe!

At the time I only knew to crochet in a circle was not the way to crochet a seashell,

so I had to make another Pattern and this is the one which works:-

It forms a hyperbolic geometric shape which folds in half to configure neatly into a shell spiral, as simple or a complex as one wishes to make.

The very first model of a seashell I made was a left hand spiral. I was disappointed, as the real thing was right hand spiral, so I taught myself to crochet left handed. It was a good exercise. I notice that many of the young girls on the school bus are left handed and one needs to know how to do it their way if I were to teach them

Then I realised-- all one needed to do was fold it back the other way to get the right hand spiral.

There was a moment when I was gazing at the folded up model and I realised that the opening was just where a snail has its opening. It was OK

Wednesday, May 26, 2010

The Fibonacci Series was named after Leonardo of Pisa, a member of the Bonacci family.Born in 1170 and died 1250.He was educated in North Africa and studied mathematics with foremost scholars. His father, Guilielmo, held a diplomatic post. In 1200 the son ended his travels and returned to Pisa.

Leonardo introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. He also introduced the Fibonacci Series to western European Mathematics.All this info I gleaned from Dr Ron Knott's website hosted by the Mathematics department of the University of Surrey, UK.www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

Thus the Fibonacci Series was not invented by Mr Bonacci.I believe that in those days The Middle East, including Baghdad, was the pinnacle of Art and Science. My guess is that the Fibonacci series goes back even further, to ancient Vedic times, when there were wise humans who understood the secrets of nature.

The best evocation of Vedic times that I have encountered is given by the Siberian Wisewoman, Anastasia, in the Ringing Cedars of Russia series, 9 books, by Vladimir Megre.http://www.ringingcedars.com/ (also .au or .ru)Especially see Book 6, "The Book of Kin", from page 94 for several chapters.

I would like to think that enough people care about Mother Earth, to help to save her and her beauty and magnificence. May it be so.

Back in August 2009 I managed to catch an interview on ABC Radio National's Artworks program, Amanda Smith chatting with Margaret Wertheim about the Exhibition at Sydney's Powerhouse Museum during Science Week . It was The Sydney Hyperbolic Crochet Reef. Hundreds of people contributed to this colorful show and you can see some of it at http://www.sydneyreef.blogspot.com/
Science meets handicrafts with a view to bring attention to the plight of coral reefs.
When doing craft, time stops.
The algorithm used was " crochet 3 stitches, increase 1 in next stitch. " It's not rigid, you can play with the numbers, to create the shapes of nature.

Then, believe it or not, I caught the moment on radio when Emma Ayres on ABC Classic Breakfast in April gave us the news that Reuters announced the winner of the 2009 Diagram Prize for the Oddest Title for a Book was "Crocheting Adventures with the Hyperbolic Plane" by Dr Daina Taimina. "Splendidly eccentric" said one newspaper, another said "superb juxtaposition...", "the two worlds collide in a captivating and completely breathless way".
You can view this elegant and erudite book on www.amazon.com/Crocheting-Adventures-Hyperbolic-Planes-Taimina/dp/1568814526
and you can see her words on http://www.hyperbolic-crochet.blogspot.com/

Hello Emma! I believe our ABC Radio has the most wonderful music and radio journalism - I listen whenever I can -- and people all over the world listen online www.abc.net.au/rn or www.abc.net.au/classic

In the 1970s and 1980s I read "The Secret Life of Plants" and :Secrets of the Soil" by Peter Tomkins and Christopher Bird. In Chapter 9 of the latter, The Vortex of Life, the Fibonacci series of numbers, 1, 2, 3, 5, 8, was mentioned. ....internal corkscrew patterns... similar to seashells and animal horns....The Vedas describe the Universe as ellipsoidal. In the 1930s a professor of Mathematics said the entire universe revolves around a geometrical form which is a rectangular hyperbola. Schwenk wrote -vortexial formative processes in nature .......
Reich wrote of the creation of matter from the throat of cosmic vortices such as nebulae.....

Back then, I thought how good it would be to make a Nautilus shell form in accordance with the Fibonacci series. Curiosity compels one to follow certain directions.

The big clue was an article in my favourite UK magazine, Resurgence. http://www.resurgence.org/ in the July/August 2007 issue, on page 43. I quote verbatim:-
"Ïn 1997 Dr Daina Taimina discovered how to make models of the geometry known as hyperbolic space using the art of crochet. Until that time most mathematicians believed it impossible to construct physical models of hyperbolic forms, yet nature has been doing just that for hundreds of millions of years. It turns out that many marine organisms embody hyperbolic geometry, among them kelps, corals, sponges and nudibranches."
The website was given of The Institute for Figuring http://www.theiff.org/
Co-directors Margaret and Christine Wertheim are curators of a splendid exhibition of Crocheted Hyperbolic Coral Reefs. (Also check out the computational origami of Robert Lang, laser physicist!). There I found more from Dr Taimina - "as you move away from a point, the space around it increases exponentially....knit or crochet...ruffle and crenellate. Íncrease 1 stitch in every 3, you get a pseudosphere- the hyperbolic equivalent of a cone.....if you increase once in every stitch it becomes increasingly crenellated....you can increase 2 or 3 times in every stitch...."

Thus I also began the adventure, trying to figure out how to crochet the Fibonacci Series.

To knit, use the same patterns but work backwards and decrease in accordance with the Fibonacci series by knitting 2 together.

With variations, the sky is the limit.
Someone could even make a huge model stuffed with pillows.
I live in a caravan on 2 acres, without electricity or a car, so I prefer small models.

One can embroider stripes up the shape.
There is a species, Nodilittorina tuberculata, which has a pattern of knobs along the spiral. I tried to copy this by regularly bunching up the edge as I sewed up.
Janthina is pale violet on top and dark violet underneath.

On Feb 14 this year, Valentine's Day, I noticed that this very same hyperbolic shape for snail shells can also configure into a bivalve! One coils the shape from the 2 pointy edges. When I have photos of complete models I will post them.

I am told that thousands of people are making crocheted hyperbolic shapes all over the world and I am glad to discover more ideas.

It took quite a bit of perseverance to sew up and pad the more complicated models, but it is not impossible!
The yellow is 4 ply equivalent cotton and the edge was made in blue sewing machine cotton.

Very fine tapestry wool, 2 ply, was used for most of the models. Half treble crochet was my preferred way. Next post will be photos of all the shapes of shells that I have made up to date, including the knitted ones.

About Me

Born in Germany January 1946 and migrated to Australia in 1949.
B.Sc from UNSW 1970.
Name is Tiiu Vanamois.
Email is tmvanam@gmail.com .
Blogs are www.awhatifworld.blogspot.com
and www.acolourfulpost.blogspot.com
and www.biomathcraft.blogspot.com.
-------The first is to do with my Land and ecology of the World.----The second is about Art and Health.----The third is mainly a study of Mathematical Series, namely Fibonacci, Lucas, Bifurcating Series. Plus varius related themes--------- Of big interest is the making of models using crochet or knitting ------if anyone is interested in working with this, please do so ------------There are two asterisks **, after all posts in date index to do with crochet or knitting or making patterns for models-------------------- 4 asterisks** ** for Tables.